Disjoint topological transitivity for weighted translations on Orlicz spaces

TL;DR

This paper characterizes when weighted translation operators on Orlicz spaces over locally compact groups exhibit disjoint topological transitivity, advancing understanding of chaos in functional analysis.

Contribution

It provides a necessary and sufficient condition for disjoint topological transitivity of weighted translations on Orlicz spaces, a novel result in operator dynamics.

Findings

Characterization of disjoint topological transitivity for weighted translations

Conditions for disjoint chaos in Orlicz spaces

Extension of operator dynamics theory to Orlicz spaces

Abstract

Let $G$ be a locally compact group, and let $\Phi$ be a Young function. In this paper, we give a sufficient and necessary condition for weighted translations on the Orlicz space $L^\Phi(G)$ to be disjoint topologically transitive. This characterization for disjoint chaos follows from the investigation on disjoint transitivity immediately.